Looking for a place to stay in NYC - questions

Hello, I'm a German guy, who is studying CS at NYU for 9 months starting September. I'd really appreciate some help from people who have some knowledge of the city in its current form.

Money is the most crucial thing for me, I don't mind if it's a very small room.

  • I heard it's best to book a place to stay for a short period of time (like 4 weeks) at the beginning and to then start searching locally for the remaining time - would you recommend that?
  • Are there any neighborhoods that I should avoid (I'm a white 26 year old male)
  • Are there any neighborhoods you would recommend
  • I know of craigslist, can you recommend other websites to find cheap rooms?
  • I have around 2000$ per month during my stay. Do you think this will be enough for everything?
  • Any other tips/recommendations/advice?

Thank you very much